Reflection-free potentials. A quantum particle moves in the potential (with p > 0) H(x + 1)ħa V(2) = 2 m a(cosh(x/a) (a)

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Reflection Free Potentials A Quantum Particle Moves In The Potential With P 0 H X 1 Ha V 2 2 M A Cosh X A A 1 (81.17 KiB) Viewed 32 times

Reflection-free potentials. A quantum particle moves in the potential (with p > 0) H(x + 1)ħa V(2) = 2 m a(cosh(x/a) (a) Find the scattering states for this problem as follows: First, set S*() = eiki ok(y) with appropriately chosen k and y = x/a. Next, substitute z = tanh y, and show that the resulting power series for Øk(2) terminates (only) if he is an integer. (b) For j = 1,2, determine the scattering states (E > 0) explicitly, and find the allowed bound states (E< 0) and their energies.